Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case

被引：78

作者：

Brasco, Lorenzo ^{[1
,2
]}

Lindgren, Erik ^{[3
]}

机构：

[1] Univ Ferrara, Dipartimento Matemat & Informat, Via Machiavelli 35, I-44121 Ferrara, Italy

[2] Aix Marseille Univ, CNRS, Cent Marseille, I2M,UMR 7373, 39 Rue Frederic Joliot Curie, F-13453 Marseille, France

[3] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

ADVANCES IN MATHEMATICS | 2017年 / 304卷

关键词：

Fractional p-Laplacian; Nonlocal elliptic equations; Besov regularity;

D O I：

10.1016/j.aim.2016.03.039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for p >= 2, solutions of equations modeled by the fractional p-Laplacian improve their regularity on the scale of fractional Sobolev spaces. Moreover, under certain precise conditions, they are in W-loc(1,p) and their gradients are in a fractional Sobolev space as well. The relevant estimates are stable as the fractional order of differentiation s reaches 1. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：300 / 354

页数：57

共 29 条

[1]

Adams R.A., 1975, Sobolev Spaces. Adams. Pure and applied mathematics

[2] A NONLOCAL p-LAPLACIAN EVOLUTION EQUATION WITH NONHOMOGENEOUS DIRICHLET BOUNDARY CONDITIONS [J].